see for instance [1]}, [2]}. By means of the subresultant theorem [3]}, we prove in Section , Theorem REF :
Given a true rank \(r\)  pair \(L\) , \(M\) , the greatest common (right) divisor for \(L-\lambda _0\)  and \(M-\mu _0\)  at any point \(P_0=(\lambda _0,\mu _0)\)  of \(\Gamma \) 
is equal to the \(r\) th differential subresultant \(\mathcal {L}_r(L-\lambda _0,M-\mu _0)\) ,
and is a differential operator of order \(r\) . In this manner we obtain an
explicit presentation of the right factor of order \(r\)  of \(L-\lambda _0\) 
and \(M-\mu _0\)  that can be effectively computed. Hence an explicit
description of the fiber \(\mathcal {F}_{P_0}\)  of the rank \(r\)  spectral sheaf \(\mathcal {F}\)  in
the terminology of [4]}, [5]}, where the operators are given in
the ring of differential operators with coefficients in the formal power
series ring \({\bf C}[[x]]\) . The factorization of ordinary differential operators using differential subresultants, for non self-adjoint operators, is an important contribution of this work.
